Frequency hopping refers to the transmission of wireless signals by rapidly switching frequencies using a pattern known to both the transmitter and the receiver. Most existing frequency hopping patterns are determined by two encryption keys, including one for the frequency domain and another for time permutation in the time domain. Such frequency hopping is beneficial because it reduces interference and/or noise and, thus, improves the success rate of signal packet transmission when transmitting a signal over a wireless communication network.
Both frequency-hopping and time-permutation keys used in the communications can reduce the probability of detection by malicious interferers or eavesdroppers. Signal interference such as partial-band tone interference (PBTI) and partial-band noise interference (PBNI) often are employed by malicious interferers to degrade the signal quality. For example, PBTI reduces the symbol error rate (SER) of the signal and degrades throughput efficiency by reducing the effective signal-to-noise ratio (SNR) of the user. Frequency hopping spread spectrum communication via pseudo random sequence key generation, in turn, is employed to make it difficult to interfere with messages. The SER of the transmitted signal is used in generating a frequency hopping pattern. However, the conventional systems and methods only approximates the symbol error rate according to simulations including, for example, the Chermoff upper bound.